Researchers designed and trained models of chemical reaction networks so that the network’s steady-state chemical composition computes a chosen input–output function. In plain terms, they asked whether a pool of reacting molecules can be made to read an environmental signal (a supplied concentration of monomers) and reliably produce a particular pattern of concentrations inside the reactor. Crucially, they kept the chemistry physically realistic: every network obeys thermodynamic rules and can be expressed in terms of energies that have clear physical meaning.

To build networks that scale, the team used polymerization chemistry built from elementary ligation (joining) and cleavage (splitting) steps. The networks include every sequence that can be made from a small “alphabet” of monomers up to some maximum length, and every possible ligation/cleavage among those sequences. The system was run in a continuously stirred tank reactor (CSTR), a simple open reactor where monomers flow in and everything is diluted at a fixed rate. Input was the concentration of monomers in the inflow, and the output was the steady-state concentration of a chosen species in the reactor.

Instead of directly tuning reaction rates, the authors trained the underlying energetic parameters that determine those rates: standard chemical potentials (which set equilibrium tendencies), transition-state energies (which set effective activation barriers), and thermodynamic drives (free-energy biases that can push the system away from equilibrium). They used implicit differentiation and a standard optimizer (Adam) to backpropagate the steady-state error against target functions and update those energetic parameters. Using this approach they fit a range of nonlinear target functions, including complex nonmonotonic polynomials; larger networks could fit harder targets. For example, a slightly larger alphabet/length network captured a quadratic “tent” shape that a smaller network could not.